Stability Analysis of Linear Time-Invariant Fractional Exponential Delay Systems

This brief presents a new approach for the stability analysis of linear fractional exponential delay systems with commensurate orders and multiple commensurate delays that enable us to decide on some cases that were previously open problems. In the proposed approach, first an auxiliary polynomial is generated by mapping the principal sheet of the Riemann surface and a pseudodelay transformation. Next, this auxiliary polynomial is employed in determining all possible purely imaginary characteristic roots for any positive time delay. Then, the concept of stability is expressed as a function of delay. Two illustrative examples are provided to demonstrate the effectiveness of the proposed method and to gain a better understanding of the problem, and the root-locus curve of these systems has been plotted as a function of time delay.